A farm settlement measures 6\text{ cm} by 8\text{ cm} on a topographical map drawn at a sc… — JAMB UTME

A farm settlement measures $6\text{ cm}$ by $8\text{ cm}$ on a topographical map drawn at a scale of $1 : 40,000$ . If the map is enlarged to a new scale of $1 : 10,000$ , what is the area of the farm settlement on the enlarged map?

$768\text{ cm}^2$ Cevap
B
$192\text{ cm}^2$
C
$12\text{ cm}^2$
D
$3\text{ cm}^2$

Cevap

The area of the farm settlement on the enlarged map is

768\text{ cm}^2

First, calculate the original area on the map:

6\text{ cm} \times 8\text{ cm} = 48\text{ cm}^2

. Next, determine the linear scale factor

n

by comparing the scale denominators:

\frac{40,000}{10,000} = 4

. Because area scale varies with the square of the linear scale, the area scale multiplier is

n^2 = 4^2 = 16

. Multiplying the original map area by

16

yields

48\text{ cm}^2 \times 16 = 768\text{ cm}^2

Adım Adım Çözüm

Calculate the original area of the farm settlement on the map.

\text{Area} = 6\text{ cm} \times 8\text{ cm} = 48\text{ cm}^2

The area on a rectangular grid is found by multiplying width by length.

Determine the linear scale factor (

n

) of the enlargement.

n = \frac{\text{Old Scale Denominator}}{\text{New Scale Denominator}} = \frac{40,000}{10,000} = 4

Enlarging a map decreases the scale denominator, increasing linear dimensions by a factor of

n

Calculate the area enlargement factor.

\text{Area Factor} = n^2 = 4^2 = 16

Area changes proportionally to the square of the linear scale factor.

Multiply the original map area by the area enlargement factor.

\text{Enlarged Area} = 48\text{ cm}^2 \times 16 = 768\text{ cm}^2

To find the new surface area on the enlarged map, multiply the initial area by

n^2

Anahtar Kavram

Map Area Enlargement and Reduction Ratio (

n^2

rule)

Tahmini Süre:1m 30s

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